This study implements and evaluates the effect of incorporating a truncated weighing function on a nonlocal plane stress projected algorithm with Tikhonov regularization for plane stress conditions.
Applying the continuum model to materials undergoing softening after yielding often results in mesh-dependent solutions. To address the mesh dependency problem, several integral-type nonlocal plasticity models have been proposed. However, the shortcoming of this approach is that only the points near the strain-softening point significantly impact its stresses and strains. Therefore, a truncated Gaussian distribution weighing function was implemented on a recently developed plane stress projected nonlocal plasticity model. The efficacy of this nonlocal formulation was measured by modifying the truncated Gaussian distribution limits as a function of the number of standard deviations and assessing the effect of this truncation on the computational time and the distribution of equivalent plastic strains. The study also analyzed the impact of the length scale and regularization parameters on the finite element solutions when the truncated weighing function is incorporated into the nonlocal plane stress projected formulation.
The output parameters, such as plastic strains, band width and force-deformation curve, showed negligible differences when the Gaussian distribution was truncated to three standard deviations, whereas the computational time decreased by around 5%. However, truncating the weighing function at two standard deviations or less increased the equivalent plastic strain. The output parameters, such as the equivalent plastic strain, are sensitive to length scale modifications and tend to converge as the regularization parameter increases.
For the first time, the present study uses the truncated Gaussian distribution as a weighing function in a 2D plane stress projected nonlocal plasticity model and studies the effect of truncation of the above function on the numerical accuracy and computational efficiency of the model. The effect of the regularization parameter will also be studied, especially for the length scale factor, since the attenuation of the Gaussian function is controlled by the standard deviation depending on the values of the length scale.
